Răspuns :
I1 . m=1
x²+x-2=0
ax²+bx+c=0, Δ=b²-4ac
x1,2=(-b+-√Δ)/2a
Δ=1-4x1x(-2)=9, √Δ=3
x1=(-1+3)/2=1
x2=(-1-3)/2=-2
2 Δ=(2m-1)²-4m(m-3)=4m²-4m+1-4m²+12m=8m+1
3. ecuatia are doua sol reale si distincte daca Δ>0, 8m+1>0, m>-1/8
II.1 f(x)=2-3x
Gf∩Ox, y=0, 2-3x=0, x=2/3 A(2/3,0)
Gf∩Oy x=0, y=2 B(0.2)
se reprezinta cele doua puncte intr-un sistem de axe xOy si se unesc cu o linie dreapta
2.f(x)=g(x)
2-3x=2x+7
5x=-5, x=-1
f(1)=2+3=5 C(-1,5)
x²+x-2=0
ax²+bx+c=0, Δ=b²-4ac
x1,2=(-b+-√Δ)/2a
Δ=1-4x1x(-2)=9, √Δ=3
x1=(-1+3)/2=1
x2=(-1-3)/2=-2
2 Δ=(2m-1)²-4m(m-3)=4m²-4m+1-4m²+12m=8m+1
3. ecuatia are doua sol reale si distincte daca Δ>0, 8m+1>0, m>-1/8
II.1 f(x)=2-3x
Gf∩Ox, y=0, 2-3x=0, x=2/3 A(2/3,0)
Gf∩Oy x=0, y=2 B(0.2)
se reprezinta cele doua puncte intr-un sistem de axe xOy si se unesc cu o linie dreapta
2.f(x)=g(x)
2-3x=2x+7
5x=-5, x=-1
f(1)=2+3=5 C(-1,5)